Suleiman was elected less than two weeks after the Lebanese government agreed to share power with Hezbollah, the Shia Islamic political group, ending a six-month presidential vacancy, CNN reported.
Suleiman succeeds President Emile Lahoud, who stepped down in November.
Lebanon's Western-backed government and the Hezbollah-led opposition reached a deal last week that observers say prevented a civil war.
Under the power-sharing agreement, a 30-member Cabinet would have 16 for the majority and 11 for the opposition and three to be filled by presidential appointment.
Suleiman has good ties with both sides of the political turmoil in Lebanon, though his ability to form a unity government remains untested, Voice of America reported
"The entire system works on consensus, so General Suleiman would have to achieve consensus on all of the important questions, and that's the most difficult problem … there's no consensus around the thorny questions, like Hezbollah's weapons," said Mohamad Bazzi of the U.S. think tank Council on Foreign Relations.
Other questions remain unsettled, notably Lebanon's relationship with Syria and Beirut's involvement in the United Nations investigation into the 2005 assassination of former Lebanese Prime Minister Rafik Hariri.